Formal Semiotic Zoo

The World-Famous UC San-Diego
Semiotic Zoo was designed to present a collection of semiotically
challenged samples of the academic discourse (announced as "captured live in the academic
jungles" :). My idea is to create here a special branch for collecting
funny samples of (i) quasi-formal academic discourse, which only looks formal but
turns out senseless under a more careful consideration; and (ii) dual
samples of quasi-reasonable discourseabout precise subjects,
which only looks reasonable but
turns out senseless under an evident and straightforward formalization.
During my wandering in the notational jungles of computer science
literature, I've encountered amazing exhibits of both types of creatures,
which could be interesting for the general public.

A typical example of quasi-reasonable discourse (which I encountered more
than once in computer science papers) is a half-page or so reasoning, which, after an
evident and direct formalization, turns out to be a "proof" that the ordinary
subset relation is transitive: If A Ì B and B
Ì C, then A Ì C. Its
"dual twin" is a popular in conceptual modeling of 90s construct of
may-be relationship between entities, postulated to be
transitive: statements A may-be B and B may-be C for concepts
A,B,C (for example, Student, Employee, Patient) imply A
may-be C. However,a bit more careful analysis reveals the
following: normally, extensions of concepts are assumed to be disjoint by default,
[[A]] Ç [[B]] = Æ, while the
statement A may-be B means the possibility [[A]]
Ç [[B]] ¹Æ (for some states of the system). Note,
however, that [[A]] Ç [[B]] ¹Æ and [[B]]
Ç [[C]] ¹ Æ do not
necessarily imply that [[A]] Ç [[C]]
¹ Æ.

There are more interesting exhibits in my archive but their
presentation needs more space. Consider, for example, the following one taken
from a big article
published in ACM TODS in 1999:

What the authors actually want to say is almost what they wrote above but the
target of the mapping A, or W in the example, is a two-element set P= {0,1}
rather than vague "statement regarding A". Indeed, in syntax we have predicate
formulas like works-for(p,c,d), whose semantic meaning are predicate
mappings like

[[works-for]]: T1´ T2´ D ® {0,1}

making formulas relations of the corresponding arity. Thus, in the example
above, P is a set {0,1} and W is a set of triples (p,c,d) (constituting,
probably, what the authors call statements) for which W(p,c,d) = 1. In other words,
W is a ternary relation presented by its characteristic function.
This simple construction is explained in any undergraduate textbook on logic.
Contrary to that, the authors say that the target set of the mapping W,
the set P, is a set of statement, that is, a relation, thus coming to an absurd. This absurd is further cast into a bold
statement:

Working in this way with formalities, the authors formulate a set of rules
for a reasonable entity-relationship (ER) modeling. As an example of their rules
applications, they consider the ER-diagrams presented below on the left and show
that it does not satisfy the Rules. Then they rebuild the diagram
according to the Rules and come to the diagram on the right. In a lengthy
consideration, the authors then state that the diagram on the right is a correct
ER-model of the universe while the left diagram is deficient.

Although the way the authors work with formalities prepares the reader for
anything possible, the result of their comparative analysis of the ER-diagrams
is still astonishing: for anyone who really worked with
ER-diagram in practical applications, the left diagram gives a quite transparent
model of the universe while the right one looks really weird. Nevertheless, the
authors so much believe in their Rules that ready to sacrifice even the ordinary
common sense. All this could be
just a funny curious sample unless it were the contents of a big
article published in a peer-reviewed and elite ACM TODS journal.

A nice sample of quasi-reasonable discourse can be found in an article
published in an ACM Communications in 2004. A detailed (and I believe
instructive) analysis of the sample can be found
here (look
here for the article itself). I submitted it to CACM but they
declined publishing saying that it was too long and technical. To make it
readable, I rearranged
the text into a short one-page article, Why 3D is Better than 2D for Representing
Spatial Figures, demonstrating the essence of the exhibit in a transparent
way. It was not accepted either :)